Factored completely, the expression 3x^2 - 3x

How does the graph of g(x) = (x − 1)3 + 5 compare to the parent function f(x) = x3?

ser-zykov [4K]

Answer:

The original function was transformed by a a horizontal shift to the right in 1 unit, and also a vertical shift upwards of 5 units.

Step-by-step explanation:

Recall the four very important rules regarding translations (shifts) of the graph of functions:

1) In order to shift the graph of a function vertically c units upwards, we must transform f (x) by adding c to it.

2) In order to shift the graph of a function vertically c units downwards, we must transform f (x) by subtracting c from it.

3) In order to shift the graph of a function horizontally c units to the right, we must transform the variable x by subtracting c from x.

4) In order to shift the graph of a function horizontally c units to the left, we must transform the variable x by adding c to x.

We notice that in our case, The original function $f(x)=x^3$ has been transformed by "subtracting 1 unit from x", and by adding 5 units to the full function. Therefore we are in the presence of a horizontal shift to the right in 1 unit (as explained in rule 3), and also a vertical shift upwards of 5 units (as explained in rule 1).

5 0

3 years ago

C) A manufacturer is making 100 times as many bows as Tess to sell in stores nationwide.

Luda [366]

1. Tess is making 12 bows.

2. 100 time as 12 bows = 100 × 12 = 1200 bows

3. In exponent form ; 12 × 10²

Given : Number of bows Tess makes = 100 times as the of x

Let the number of bows Tess makes be x

Thus the number of bows Tess is making is 12.

100 times as many means the number which we have calculated should be multiplied by 100.

thus the number as w2e have found out is 12

so multiplied by 100 will give us 1200

Exponential form means that the given number should be expressed in the form of 10.

As the number which is given to us is 1200n

thus in exponential form we can write it as 12 multiplied by 10 raise to the power as the number of zeros of present.

Here then number of number of zeros is 2

thus 10 raised to the power 2.

To know more about expression and exponents you may visit the link which is mentioned below:

brainly.com/question/27850853

#SPJ13

6 0

1 year ago

How do you do inequalities

fgiga [73]

So some quick tips for inequalities:
**What you do to one side you HAVE TO do it to the other 2**
**If you ever divide a negative number past the inequality signs, the signs FLIP!!**
(e.g. 2>-5x>25)
-2/5 <x < -5

I hope that this has helped!

8 0

2 years ago

18 POINTS MATH HELP PLEASE

lyudmila [28]

Answer:

yes it is safe

Step-by-step explanation:

so if you d base times hight you will get 27 witch is the degrees of witch the triangle it creates

7 0

3 years ago

You collect a total of $75 in donations from three people. The three donations are in the ratio 4 : 4 : 7. (hint: set up an equa

Amanda [17]

Answer:

Step-by-step explanation:

Since the ratio is 4x:4x:7x, if we add all those numbers up we get 15. Then we do 75/15 to get what x equals. So we get 5. So x equals 5. Following the rules of multiplication, you do 4(5):4(5):7(5), and simplifying that further, you get 20:20:35. If we add all those values up, we should get 75, and we do!

If you're wondering why I did 4x:4x:7x instead of 4:4:7, it's because a ratio is just a...well ratio? It's easier to visualize if you put a variable because the variable could be anything, and you would have to multiply all the given values to get the same proportions. In summery, I did it so it was easier to visualize

3 0

3 years ago

Factored completely, the expression 3x^2 - 3x - 18 is equivalent to